1 | Page INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500 043 CIVIL ENGINEERING QUESTION BANK Course Name : Probability and Statistics Course Code : A40008 Class : II-II B. Tech Branch : CIVIL Engineering Year : 2016 - 2017 Course Faculty : Ms. B PRAVEENA OBJECTIVES To meet the challenge of ensuring excellence in engineering education, the issue of quality needs to be addressed, debated and taken forward in a systematic manner. Accreditation is the principal means of quality assurance in higher education. The major emphasis of accreditation process is to measure the outcomes of the program that is being accredited. In line with this, Faculty of Institute of Aeronautical Engineering, Hyderabad has taken a lead in incorporating philosophy of outcome based education in the process of problem solving and career development. So, all students of the institute should understand the depth and approach of course to be taught through this question bank, which will enhance learner’s learning process. 1. Group - A (Short Answer Questions) S. No Question Blooms Taxonomy Level Course Outcome UNIT-I SINGLE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 1 If X & Y is a random variable then Prove E[X+K]= E[X]+K ,where ‘K’ constant Understand b 2 Prove that 2 2 2 ) ( X E Understand b 3 Explain probability distribution for discrete and continuous Analyze c 4 If X is Discrete Random variable then Prove that Var (a X +b) = a 2 var(X) Understand c 5 Write the properties of the Normal Distribution Analyze e 6 Write the importance and applications of Normal Distribution Apply e 7 Define different types of random variables with example Remember c 8 Derive variance of binomial distribution Evaluate d 9 Derive mean of Poisson distribution Evaluate d 10 Explain about Moment generating function Analyze e UNIT-II
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1 | P a g e
INSTITUTE OF AERONAUTICAL ENGINEERING
Dundigal, Hyderabad - 500 043
CIVIL ENGINEERING
QUESTION BANK
Course Name : Probability and Statistics
Course Code : A40008
Class : II-II B. Tech
Branch : CIVIL Engineering
Year : 2016 - 2017
Course Faculty : Ms. B PRAVEENA
OBJECTIVES
To meet the challenge of ensuring excellence in engineering education, the issue of quality needs to be
addressed, debated and taken forward in a systematic manner. Accreditation is the principal means of
quality assurance in higher education. The major emphasis of accreditation process is to measure the
outcomes of the program that is being accredited.
In line with this, Faculty of Institute of Aeronautical Engineering, Hyderabad has taken a lead in
incorporating philosophy of outcome based education in the process of problem solving and career
development. So, all students of the institute should understand the depth and approach of course to be
taught through this question bank, which will enhance learner’s learning process.
1. Group - A (Short Answer Questions)
S. No Question Blooms Taxonomy
Level
Course
Outcome
UNIT-I
SINGLE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
1 If X & Y is a random variable then Prove E[X+K]= E[X]+K
,where ‘K’ constant
Understand b
2 Prove that 222 )( XE Understand b
3 Explain probability distribution for discrete and continuous
Analyze c
4 If X is Discrete Random variable then Prove that Var (a X +b) = a
2
var(X) Understand c
5 Write the properties of the Normal Distribution Analyze e
6 Write the importance and applications of Normal Distribution Apply e
7 Define different types of random variables with example
Remember c
8 Derive variance of binomial distribution Evaluate d
9 Derive mean of Poisson distribution Evaluate d
10 Explain about Moment generating function Analyze e
UNIT-II
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S. No Question Blooms Taxonomy
Level
Course
Outcome
MULTIPLE RANDOM VARIABLES, CORRELATION ®RESSION
1 State the properties of joint distribution function of two random
variable Analyze e
2 Explain about random vector concepts
Analyze f
3 If a random variable W=X+Y where X and Y are two independent
random variables what is the density function of W Analyze f
4 Explain types of correlations Remember g
5 Write the properties of rank correlation coefficient Analyze g
6 Write the properties of regression lines Analyze g
7 Write the difference between correlation and regression Remember g
8 The rank correlation coefficient between the marks in two subjects
is 0.8.the sum of the squares of the difference between the ranks is
33.find the number of students
Evaluate g
9 Find the angle between the regression lines if S.D of Y is twice the
S.D of X and r=0.25 Evaluate g
10 Derive the angle between the two regression lines Evaluate
UNIT-III
SAMPLING DISTRIBUTIONS AND TESTING OF HYPOTHESIS
1 Explain different Types and Classification of sampling
Analyze h
2 Write about Point Estimation, Interval Estimation
understand i
3 Write a short note on Hypothesis, Null and Alternative with
suitable examples understand i
4 Write a short Note on Type I & Type II error in sampling theory understand i
5 Prove that Sample Variance is not an Unbiased Estimation of
Population Variance understand i
6 Write Properties of t-distribution
Analyze j
7 Explain about Chi-Square Analyze j
8 Write a short note on Distinguish between t,F, Chi square test understand j
9 Explain about Bayesian estimation Analyze i
10 Compare Large Samples and Small sample tests Create j
UNIT-IV
QUEUING THEORY
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S. No Question Blooms Taxonomy
Level
Course
Outcome
1 Explain queue discipline
Analyze k
2 Explain pure birth process
Analyze k
3 Explain pure death process
Analyze k
4 Derive expected number of customers
Evaluate k
5 Derive average waiting time in queue
Evaluate l
6 Evaluate P(n>1)
Evaluate l
7 Define transient state and steady sate Remember l
8 Explain M/M/1 model
Analyze l
9 Explain M/M/1 with infinite population Analyze l
10 Derive probability of having n customers Pn in a queue M/M/1,
having poisson arrival Evaluate l
UNIT-V
STOCHASTIC PROCESSES
1 Define stochastic process Remember m
2 Explain different types of stochastic process Analyze m
3 Give examples of stochastic process Create m
4 Find the expected duration of the game for double stakes Evaluate m
5 Define Markov’s chain Understand m
6 Explain Markov’s property Understand m
7 Explain transition probabilities Understand m
8 Explain stationary distribution Understand m
9 Explain limiting distribution Understand m
10 Explain irreducible and reducible Understand m
1. Group - B (Long Answer Questions)
S. No Question Blooms Taxonomy
Level
Course
Outcome
UNIT-I
SINGLE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
1 A random variable x has the following probability function: Evaluate c
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S. No Question Blooms Taxonomy
Level
Course
Outcome
x 0 1 3 4 5 6 7
P(x) 0 k 2k 2k 3k k2
7k2+k
Find the value of k (ii) evaluate p(x<6), p( x>6)
2 Let X denotes the minimum of the two numbers that appear when
a pair of fair dice is thrown once. Determine the (i) Discrete
probability distribution (ii) Expectation (iii) Variance
Understand &
Evaluate c
3 A random variable X has the following probability function:
X -2 -1 0 1 2 3
P(x
)
0.1 K 0.2 2K 0.3 K
Then find (i) k (ii) mean (iii) variance (iv) P(0 < x < 3)
Evaluate c
4 A continuous random variable has the probability density
function
, 0, 0( )
0,
xkxe for xf x
otherwise
Determine (i) k (ii) Mean
(iii) Variance
Evaluate c
5 If the PDF of Random variable f(x) = 10,1 2 xxk then
find (i) k (ii) p[0.1<x<0.2] (iii) P[x>0.5] Evaluate c
6 If the masses of 300 students are normally distributed with mean
68 kg and standard deviation3 kg how many students have
masses: greater than 72 kg (ii) less than or equal to 64 kg (iii)
between 65 and 71 kg inclusive
Analyze e
7 Out of 800 families with 5 children each, how many would you
expect to have (i)3 boys (ii)5 girls (iii)either 2 or 3 boys ?
Assume equal probabilities for boys and girls.
Understand &
Evaluate d
8 If a Poisson distribution is such that
3( 1). ( 3)
2P X P X ,
find (i) ( 1)P X (ii) ( 3)P X (iii) (2 5)P X .
Evaluate d
9 Average number of accidents on any day on a national highway
is 1.8. Determine the probability that the number of accidents is
(i) at least one (ii) at most one
Analyze &
Evaluate d
10 In a Normal distribution, 7% of the item are under 35 and 89% Evaluate e
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S. No Question Blooms Taxonomy
Level
Course
Outcome
are under 63. Find the mean and standard deviation of the
distribution.
UNIT-II
MULTIPLE RANDOM VARIABLES, CORRELATION ®RESSION
1 Consider the joint probability density function f(x, y) = xy, 0 < x
< 1, 0 < y < 2. Find marginal density function Evaluate f
2 Two independent variable X and Y have means 5 and 10 and
variances 4 and 9 respectively. Find the coefficient of correlation
between U and V where U=3x+4y, V=3x-y
Understand &
Evaluate g
3 The probability density function of a random variable x is
f xx
x( ) exp ,
1
2 20 . Find the probability of 1 < x < 2.
Evaluate f
4 Let X and Y random variables have the joint density function
f(x, y)=2,0<x<y<1then find marginal density function Evaluate f
5 Find the rank correlation coefficient for the following ranks of 16